Iteroparous reproduction strategies and population dynamics

Asymptotic relationships between a class of continuous partial differential equation population models and a class of discrete matrix equations are derived for iteroparous populations. First, the governing equations are presented for the dynamics of an individual with juvenile and adult life stages. The organisms reproduce after maturation, as determined by the juvenile period, and at specific equidistant ages, which are determined by the iteroparous reproductive period. A discrete population matrix model is constructed that utilizes the reproductive information and a density-dependent mortality function. Mortality in the period between two reproductive events is assumed to be a continuous process where the death rate for the adults is a function of the number of adults and environmental conditions. The asymptotic dynamic behaviour of the discrete population model is related to the steady-state solution of the continuous-time formulation. Conclusions include that there can be a lack of convergence to the steady-state age distribution in discrete event reproduction models. The iteroparous vital ratio (the ratio between the maximal age and the reproductive period) is fundamental to determining this convergence. When the vital ratio is rational, an equivalent discrete-time model for the population can be derived whose asymptotic dynamics are periodic and when there are a finite number of founder cohorts, the number of cohorts remains finite. When the ratio is an irrational number, effectively there is convergence to the steady-state age distribution. With a finite number of founder cohorts, the number of cohorts becomes countably infinite. The matrix model is useful to clarify numerical results for population models with continuous densities as well as delta measure age distribution. The applicability in ecotoxicology of the population matrix model formulation for iteroparous populations is discussed.     

Stabilization of population dynamics via threshold harvesting strategies

We study two different harvesting/thinning control strategies in the framework of one-dimensional discrete time population models. They have the common feature of considering a threshold population size, commonly called Biomass at the limit, under which the population is not altered, and they differ in how the harvesting/thinning is applied when that threshold is surpassed: one uses the well known proportional feedback control, whereas the other employs the recently proposed target oriented control. We focus on the possibility of applying these strategies to control the chaotic behaviour predicted by some one-dimensional discrete time population models. We discuss the basic properties of both strategies and compare them with other simpler control methods. Particularly, we show that increasing the threshold does not affect, or almost does not affect, a stable exploited population as long as the threshold is lower than the carrying capacity of the system.     

Evolution and population dynamics in stochastic environments

Inter-generational temporal variability of the environment is important in the evolution and adaptation of phenotypic traits. We discuss a population-dynamic approach which plays a central role in the analysis of evolutionary processes. The basic principle is that the phenotypes with the greatest long-term average growth rate will dominate the entire population. The calculation of longterm average growth rates for populations under temporal stochasticity can be highly cumbersome. However, for a discrete non-overlapping population, it is identical to the geometric mean of the growth rates (geometric mean fitness), which is usually different from the simple arithmetic mean of growth rates. Evolutionary outcomes based on geometric mean fitness are often very different from the predictions based on the usual arithmetic mean fitness. In this paper we illustrate the concept of geometric mean fitness in a few simple models. We discuss its implications for the adaptive evolution of phenotypes, e.g. foraging under predation risks and clutch size. Next, we present an application: the risk-spreading egg-laying behaviour of the cabbage white butterfly, and develop a two-patch population dynamic model to show how the optimal solution diverges from the ssual arithmetic mean approach. The dynamics of these stochastic models cannot be predicted from the dynamics of simple deterministic models. Thus the inclusion of stochastic factors in the analyses of populations is essential to the understanding of not only population dynamics, but also their evolutionary dynamics.     

Consequences of behavioral dynamics for the population dynamics of predator-prey systems with switching

This article explores how different mechanisms governing the rate of change of the predators preference alter the dynamics of predator-prey systems in which the predator exhibits positive frequency-dependent predation. The models assume that individuals of the predator species adaptively adjust a trait that determines their relative capture rates of each of two prey species. The resulting switching behavior does not instantaneously attain the optimum for current prey densities, but instead lags behind it. Several mechanisms producing such lags are discussed and modeled. In all cases examined, our question is whether a realistic behavioral lag can significantly change the dynamics of the system relative to an analogous case in which the predators switching is effectively instantaneous. We also explore whether increasing the rate parameters of dynamic models of behavior results in convergence to the population dynamics of analogous models with instantaneous switching, and whether different behavioral models produce similar population dynamics. The analysis concentrates on systems that undergo endogenously generated predator-prey cycles in the absence of switching behavior. The average densities and the nature of indirect interactions are often sensitive to the rate of behavioral change, and are often qualitatively different for different classes of behavioral models. Dynamics and average densities can be very sensitive to small changes in parameters of either the prey growth or predator switching functions. These differences suggest that an understanding of switching in natural systems will require research into the behavioral mechanisms that govern lags in the response of predator preference to changes in prey density.     

核桃-小麦复合系统中细根生长动态及竞争策略

以核桃(Juglans regia)-小麦(Triticum aestivum)间作复合系统为研究对象,用微根窗和根钻相结合的方法采样,研究复合系统中核桃和小麦细根年内年际的生长动态和竞争适应策略,为农林复合系统的经营管理和竞争模型的建立提供理论依据和技术支持。结果表明,间作核桃和小麦根系均在上半年有一个大的生长高峰(5月和4月),在下半年有一个小的生长高峰(9月和11月),二者的竞争主要发生在上半年的大生长高峰期。在各年份各土层,间作核桃的根长密度均低于单作核桃,且在从第7年开始存在显著差异。在0—20 cm土层间作小麦根长密度在第3—7年间获得迅速提高,从第7年开始显著高于单作小麦,但在20 cm以下土层则相反。间作使核桃和小麦细根生态位实现了分离,11年的观察期内间作核桃比单作核桃细根的垂直分布中心下移了6.59 cm,间作小麦比单作小麦的上移了8.59 cm。在根系竞争策略方面,小麦根系是通过短期内的快速生长,迅速占据土壤空间获得竞争优势;而核桃根系是通过根系的逐年积累,逐步占据土壤空间从而获得竞争优势。可以干扰核桃根系积累过程的"竞争-干扰-再平衡"农林复合经营管理策略可以让复合系统中核桃和小麦保持各自竞争优势的情况下实现共存。在根系形态方面,自身细根直径较小者小麦在剧烈竞争区域以增加细根直径减小比根长来适应竞争,而自身细根直径较大者核桃则相反。     

Static behavioral effects on gonorrhea transmission dynamics in a MSM population

An SIS/SAS model of gonorrhea transmission in a population of highly active men-having-sex-with-men (MSM) is presented in this paper to study the impact of safe behavior on the dynamics of gonorrhea prevalence. Safe behaviors may fall into two categories—prevention and self-awareness. Prevention will be modeled via consistent condom use and self-awareness via STD testing frequency. Stability conditions for the disease free equilibrium and endemic equilibrium are determined along with a complete analysis of global dynamics. The control reproductive number is used as a means for measuring the effect of changes to model parameters on the prevalence of the disease. We also find that appropriate intervention would be in the form of a multifaceted approach at overall risk reduction rather than tackling one specific control individually.     

Relatedness and competitive asymmetry – implications for growth and population dynamics

The members of natural populations often differ in size and relatedness to each other, which may affect the division of limited resources and have consequences on reproductive success and population dynamics. We modeled seasonal growth and dynamics in populations composed of different types of relatives (full-sibs, half-sibs and non-related individuals) under the continuum of competitive scenarios between complete symmetry and asymmetry. Growth was assumed logistic in proportion to individual biomass and the size-differences were weighted by the relatedness of individuals. The symmetric component of competition was experienced by all individuals in proportion to their biomass, whereas the asymmetric component was individual-specific, and influenced only by the individuals larger than the focal individual. Relatedness decreased and competitive asymmetry increased the variability of individual biomasses. Mortality of the smallest individuals and the size threshold of reproduction decreased population density. Population dynamics were stable when there was no size threshold for reproduction but the presence of the threshold led to cyclic dynamics under low competitive asymmetry. The effects of the threshold were greater among related than unrelated individuals. The results suggest that individual differences and the asymmetry of competition can greatly affect population dynamics. Full symmetry of competition may be evolutionarily unstable in populations of related individuals as it may increase the probability of extinction due to demographic stochasticity.     

Evolution, population dynamics, and stability: A comment

A recently proposed criterion for community coevolution is shown to be equivalent to requiring that a mutant have a positive selective advantage if it is to spread through a population. This is one of the basic conclusions of deterministic population genetics.     

Restoring species through reintroductions: strategies for source population selection

Only a quarter of reintroduction programs succeed in restoring a self‐sustaining population of an extirpated species. Optimal source population selection for restoration efforts can increase the fitness of translocated individuals and improve reintroduction success. Here, we describe the support for two strategies for selecting source populations: pre‐existing adaptation and adaptive potential. The pre‐existing adaptation strategy focuses on source populations with a high frequency of genotypes that confer adaptations, and within this strategy we detail the ancestry matching approach and environment matching approach. The adaptive potential strategy focuses on source populations with high heritable genetic variation that confer the potential to adapt, and within this strategy we detail the single source population approach and multiple source population approach. We review empirical tests of the different approaches, and find stronger support for the pre‐existing adaptation strategy than the adaptive potential strategy. We provide a framework for source population selection based on the two strategies, highlighting the importance of gathering information on key environment features in the source and restoration locations, as well as detail the knowledge gaps. Filling these knowledge gaps is important for validating and potentially revising our proposed framework, and ultimately improving the success rate of restoring extirpated populations.     

Evolution of rotifer population dynamics in a heterogeneous habitat: mathematical modeling

We present the results of mathematical modeling of a rotifer species inhabiting two coupled habitats with different environmental conditions. We use the modified Consensus model and show that the exchange between the habitats can lead to chaotization of originally regular plankton dynamics and synchronization of plankton biomass oscillations. As a result, the invasion of a chaotic regime takes place.     

Evolution of reproductive effort in viscous populations: the importance of population dynamics

I present two ecological models for the evolution of reproductive effort in viscous populations with empty sites. In contrast with previous studies, I show that limited dispersal needs not have a positive effect on the evolutionarily stable allocation of resources to fecundity versus survival. Rather, depending on the feedback between the trait and the population dynamics, population viscosity may have no effect or even lead to a decrease in the evolutionarily stable reproductive effort when individuals can degrade their environment during their lifetime. I show that the different evolutionary outcomes can be explained by the asymmetry in the level of kin competition resulting from investing into juveniles or into adults.     

Evolution of virulence driven by predator-prey interaction: Possible consequences for population dynamics

The evolution of pathogen virulence in natural populations has conventionally been considered as a result of selection caused by the interactions of the host with its pathogen(s). The host population, however, is generally embedded in complex trophic interactions with other populations in the community, in particular, intensive predation on the infected host can increase its mortality, and this can affect the course of virulence evolution. Reciprocally, in the long run, the evolution of virulence within an infected host can affect the patterns of population dynamics of a predator consuming the host (e.g. resulting in large amplitude oscillations, causing a severe drop in the population size, etc.). Surprisingly, neither the effect of predation on the evolution of virulence within a host, nor the influence of the evolution of virulence upon the consumer's dynamics has been addressed in the literature yet. In this paper, we consider a classical S-I ecoepidemiological model in which the infected host is consumed by a predator. We are particularly interested in the evolutionarily stable virulence of the pathogen in the model and its dependence upon ecologically relevant parameters. We show that predation can prominently shift the evolutionarily stable virulence towards more severe strains as compared to the same system without predation. We demonstrate that the evolution of virulence can result in a succession of dynamical regimes and can even lead to the extinction of the predator in the long run. The presence of a predator can indirectly affect the evolution within its prey since the evolutionarily stable virulence becomes a function of the prey growth rate, which would not be the case in a predator-free system. We find that the evolutionarily stable virulence largely depends on the carrying capacity K of the prey in a non-monotonous way. The model also predicts that in an eutrophic environment the shift of virulence towards evolutionarily stable benign strains can cause demographically stochastic evolutionary suicide, resulting in the extinction of both species, thus artificially maintaining severe strains of pathogen can enhance the persistence of both species.     

Evolution of resource specialisation in competitive metacommunities

Spatial environmental heterogeneity coupled with dispersal can promote ecological persistence of diverse metacommunities. Does this premise hold when metacommunities evolve? Using a two‐resource competition model, we studied the evolution of resource‐uptake specialisation as a function of resource type (substitutable to essential) and shape of the trade‐off between resource uptake affinities (generalist‐ to specialist‐favouring). In spatially homogeneous environments, evolutionarily stable coexistence of consumers is only possible for sufficiently substitutable resources and specialist‐favouring trade‐offs. Remarkably, these same conditions yield comparatively low diversity in heterogeneous environments, because they promote sympatric evolution of two opposite resource specialists that, together, monopolise the two resources everywhere. Consumer diversity is instead maximised for intermediate trade‐offs and clearly substitutable or clearly essential resources, where evolved metacommunities are characterised by contrasting selection regimes. Taken together, our results present new insights into resource‐competition‐mediated evolutionarily stable diversity in homogeneous and heterogeneous environments, which should be applicable to a wide range of systems.     

Evolution of life-history traits collapses competitive coexistence

Trade-offs between competitive ability and the other life-history traits are considered to be a major mechanism of competitive coexistence. Many theoretical studies have demonstrated the robustness of such a coexistence mechanism ecologically; however, it is unknown whether the coexistence is robust evolutionarily. Here, we report that evolution of life-history traits not directly related to competition, such as longevity, and predator avoidance, easily collapses competitive coexistence in several competition systems: spatially structured, and predator-mediated two-species competition systems. In addition, we found that a superior competitor can be excluded by an inferior one by common mechanisms among the models. Our results suggest that ecological competitive coexistence due to a life-history trait trade-off balance may not be balanced on an evolutionary timescale, that is, it may be evolutionarily fragile.     

On selection dynamics for competitive interactions

In this paper, we are interested in an integro-differential model that describe the evolution of a population structured with respect to a continuous trait. Under some assumption, we are able to find an entropy for the system, and show that some steady solutions are globally stable. The stability conditions we find are coherent with those of Adaptive Dynamics.     

Chemical amplification through competitive autocatalysis

Linear stability analysis shows that in a theoretical system, which consists of two first order and two autocatalytic reactions, symmetry breaking takes place under certain circumstances. Total separation can be achieved if the stabilizing first order reactions are omitted from the mechanism.